SOLUTION: Twelve presidents, 5 males and 7 females, attending a summit on climate decide to conclude the summit with a photo shoot. In how many ways different can they arrange themselves in
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Question 1162135: Twelve presidents, 5 males and 7 females, attending a summit on climate decide to conclude the summit with a photo shoot. In how many ways different can they arrange themselves in a single row, if the males must be kept together?
The answer is 8*5!*7! = 8*(5*4*3*2*1)*(7*6*5*4*3*2*1) = 4838400.
Explanation
We consider the group of 5 males as one object.
There are 8 possible positions/places for this group, considered as a single object, in the row of 7 females.
It gives the first factor of 8 in the formula.
Next, there are 5! ways to order 5 males inside their group.
It gives the factor 5! in the formula.
Finally, there are 7! ways to order 7 females inside their group.
It gives the factor 7! in the formula.
All these elementary arrangements are INDEPENDENT - - - so, we take the product of the factors to get the answer.
